Expansions and Asymptotics for StatisticsAsymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti |
Contents
Introduction | 1 |
General series methods | 23 |
Pade approximants and continued fractions | 75 |
The delta method and its extensions | 99 |
Optimality and likelihood asymptotics | 143 |
The Laplace approximation and series | 193 |
The saddlepoint method | 227 |
Summation of series | 279 |
Glossary of symbols | 321 |
Useful limits series and products | 325 |
| 327 | |
| 331 | |
Back Cover | 344 |
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Common terms and phrases
analytic apply assumptions asymptotic expansion asymptotic risk asymptotic series asymptotically normal calculate chapter coefficients compute consider constant continued fraction contour cumulants defined Definition delta method density function derivatives differentiable distribution function divergent series diverges enh(x enveloping series equation evaluated example exponential finite formula function f(x h(Xn identically distributed independent integral integrand Laplace Laplace approximation Let X1 locally asymptotically log-likelihood lower bound Maple maximum likelihood estimator mean normal distribution notation obtained Padé approximants parameter partial sums Poisson polynomial power series probability Problem proof properties Proposition Prove quadratic Raabe's test random sample random variables ratio rational function reader real numbers remainder term result saddle-point approximation saddle-point method sequence statistic Stirling's approximation Suppose theorem transformation unbiased variance write zero Εθο θη θο μα πη σ˛ Χη